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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to \infty } \sqrt x (\sqrt {x + 5} - \sqrt x ) = $
  • A
    $5$
  • B
    $3$
  • ✓
    $5/2$
  • D
    $3/2$
✓

Answer

Correct option: C.
$5/2$
c
(c) $\mathop {\lim }\limits_{x \to \infty } \,\sqrt x \,(\sqrt {x + 5} - \sqrt x ) \times \frac{{(\sqrt {x + 5} + \sqrt x )}}{{(\sqrt {x + 5} + \sqrt x )}}$

$ = \mathop {\lim }\limits_{x \to \infty } \frac{{\sqrt x \,(5)}}{{\sqrt x \,\left( {\sqrt {1 + \frac{5}{x}} + 1} \right)}} = \frac{5}{2}$.

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